Inverse Functions (Tables & Graphs)

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to x.

Tags

CCSS.HSF-BF.B.4A

Front

How can you determine if two functions are inverses of each other?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

What does it mean if two functions are not inverse functions?

Back

If f(g(x)) ≠ x or g(f(x)) ≠ x for any x in the domain, then the functions are not inverses.

Tags

CCSS.HSF-BF.B.4B

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and then solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of an inverse function?

Back

The range of the inverse function is the domain of the original function.

Tags

CCSS.HSF-BF.B.4C

Front

What is the significance of the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one, which is necessary for it to have an inverse.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input.

Front

How do you graph the inverse of a function?

Back

To graph the inverse, reflect the graph of the original function across the line y = x.

Tags

CCSS.HSF-BF.B.4C